$y = C e ^ { 4 x ^ { 2 } }$

question 38

Short Answer

$y = C e ^ { 4 x ^ { 2 } }$ is the solution of the differential equation $y ^ { \prime } = 8 x y$ . Find the solution that satisfies the initial condition $y ( 1 ) = 1$ .

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Definitions:

Total Social Benefit

The total benefit to society from producing or consuming a good, including both private benefits and any external benefits.

Total Individual Benefit

The total value or satisfaction that an individual derives from consuming a particular quantity of goods or services.

Marginal Benefit

The supplementary enjoyment or advantage gained by consuming another unit of a good or service.

Marginal Social Benefit

The additional benefit received by society as a whole from the production or consumption of one more unit of a good.